Select the coordinates A' and B' after dilation of the line segment AB with a scale factor of 1/3, centered at the origin where the end points are A (-6, 3) and B (-12, 9).
To find the coordinates A' and B' after dilation of the line segment AB with a scale factor of 1/3, we can use the following formula:
A' = (k * (A - O) ) + O
B' = (k * (B - O) ) + O
Where:
- A' and B' are the new coordinates after dilation.
- k is the scale factor.
- A and B are the original coordinates of the line segment endpoints.
- O is the center of dilation, which is (0, 0) in this case since it is centered at the origin.
Now let's plug in the values:
A' = (1/3 * (-6, 3 - (0, 0))) + (0, 0)
= (1/3 * (-6, 3)) + (0, 0)
= (-6/3, 3/3) + (0, 0)
= (-2, 1) + (0, 0)
= (-2, 1)
B' = (1/3 * (-12, 9 - (0, 0))) + (0, 0)
= (1/3 * (-12, 9)) + (0, 0)
= (-12/3, 9/3) + (0, 0)
= (-4, 3) + (0, 0)
= (-4, 3)
Therefore, the coordinates A' after dilation are (-2, 1) and the coordinates B' after dilation are (-4, 3).